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master's thesis
Metoda unutrašnje točke u kvadratičnom programiranju
Zagreb: University of Zagreb, Faculty of Science, 2019. urn:nbn:hr:217:840114
Marodi, Petra
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

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Marodi, P. (2019). Metoda unutrašnje točke u kvadratičnom programiranju (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:840114

Marodi, Petra. "Metoda unutrašnje točke u kvadratičnom programiranju." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:840114

Marodi, Petra. "Metoda unutrašnje točke u kvadratičnom programiranju." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:840114

Marodi, P. (2019). 'Metoda unutrašnje točke u kvadratičnom programiranju', Master's thesis, University of Zagreb, Faculty of Science, accessed 04 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:840114

Marodi P. Metoda unutrašnje točke u kvadratičnom programiranju [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2019 [cited 2024 November 04] Available at: https://urn.nsk.hr/urn:nbn:hr:217:840114

P. Marodi, "Metoda unutrašnje točke u kvadratičnom programiranju", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:217:840114

Metadata
TitleMetoda unutrašnje točke u kvadratičnom programiranju
AuthorPetra Marodi
MentorMarko Vrdoljak (mentor)
Committee memberMarko Vrdoljak (predsjednik povjerenstva)
Committee memberJosip Tambača (član povjerenstva)
Committee memberNenad Antonić (član povjerenstva)
Committee memberNela Bosner (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2019-09-26, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu opisuje se metoda unutrašnje točke, odnosno primarno-dualna metoda centralnog puta i primjenjuje se na zadaće linearnog i kvadratičnog programiranja. Za linearno programiranje navode se uvjeti optimalnosti i uvodi se pojam centralnog puta. Detaljno se analizira Newtonova metoda na kojoj se temelji metoda unutrašnje točke i u tu svrhu koriste se ortogonalne projekcije. Navodi se algoritam nalaženja optimalne točke i dokazuje se rezultat o njegovoj točnosti i broju iteracija. Za kvadratično programiranje najprije se dokazuju nužni i dovoljni uvjeti za optimalnost i opisuje se metoda centralnog puta uz modifikaciju Newtonove metode. Uvodi se pojam okoline centralnog puta i na temelju toga navode se dva algoritma primarno-dualne metode centralnog puta: metoda kratkog koraka i metoda dugog koraka, koja se demonstrira na konkretnom primjeru.
Abstract (english)
In this paper we explain the interior point method, i.e. primal-dual path-following method and apply it to linear and quadratic optimization problems. For linear programming we formulate optimality conditions and introduce the term of central path. We analyze Newton’s method which is usually used in many interior point methods and for this purpose we use orthogonal projections. We describe algorithm of primal-dual interior point method and prove the result of its accuracy and number of iterations. For quadratic programming we first prove necessary and sufficient optimality conditions and describe the central path method with some modifications of Newton’s method. We introduce the term of neighborhood of the central path and based on that we describe two algorithms: short-step path-following method and long-step path-following method, which we demonstrate on example.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:840114
Study programmeTitle: Finance and Business Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2020-02-07 13:05:20